Comparisons of Different Disk Functions Based on Laboratory Bidirectional Reflectance Measurements of Lunar-Type Minerals and Lunar Soils

In photometric modeling, disk function plays a crucial role in describing scattering behaviors related to the local incidence and emission angles of an observed surface. Finding a proper disk function is important for normalizing spectra observed under different observing geometries. This study evaluates the performances of five different disk functions, including the Lommel-Seeliger function, and functions proposed by Minnaert, McEwen, and Akimov, using bidirectional reflectance distribution function (BRDF) data of lunar-type minerals and Apollo lunar soils. BRDF measurements of olivine, orthopyroxene, plagioclase, and ilmenite were conducted to examine the effects of mineralogy and particle size. Our results indicate that the Akimov empirical function is most effective in reducing discrepancies among data measured under varied incidence and emission angles for both pure minerals and lunar soil samples. Two empirical functions for the free parameter q in this model were generalized based on pure mineral data, but are unsuitable for lunar soil samples. The q derived for six Apollo lunar soil samples are much lower than those for pure silicate minerals but align well with remote sensing observations, with no distinct differences between lunar mare and highland soil samples, possibly due to extensive space weathering on the lunar surface. The q values at a phase angle of 70° show the strongest correlation with the widely used maturity index I_s/FeO, and two empirical functions between I_s/FeO and q(70°) for bands 550 and 750 nm were established, which may be used to quantify the degree of space weathering.